1. Introduction

Housing prices are crucial to people's life and have always been an important indicator and public concern. Since 2004, housing prices nationwide have been continuously rising: housing price in China experienced unprecedented growth from 2002 to 2010, by nearly 1.5 times and seems to be stabilizing recently [1, 2]. The daily consumption of residents in both China's urban and rural regions were affected by the high private housing prices in the real estate sector. However, the public is not particularly aware of the influencing factors [3]. This paper analyzes the various potential factors that may affect the housing prices in Shanghai, in attempt to help residents with tools to assess and predict the trend of housing prices in Shanghai, and possibly other cities in China.

The real estate sector is a sophisticated regime: a myriad of factors may contribute to the mobile housing prices. Housing price assessment and prediction is also a subject of research academia. Lü claims that area of the houses is significant for analyzing the development of the Chinese real estate market [4]. Yan et al. also used housing price dataset in Beijing, combining the hedonic models, the lasso regression, and the random forests in their analysis, and optimizing their results [5]. They studied such variables as the number of living rooms, bedrooms, and bathrooms on housing prices. The combination of multiple tools increased the accuracy and reliability of their analysis. As for second-hand houses, Zhen et al. suggested that the availability of elevators is an important factor for prices, as shown in their study of Chengdu [6]. Multiple linear regression, decision trees, and extreme gradient boosting models are used to fit the price prediction curve of influencing factors. The XGBoost algorithm stands out, when compared with other models, as the most accurate, widely applicable, and reliable in data prediction, while reducing overfitting. However, it might slightly lack precision when analyzing results. Domestic scholars believed that the structure and the age of the buildings are among the influencing factors for housing prices [6, 7]. It is claimed by Zheng that the renovation of the houses is a crucial factor leading to differences of their prices [8]. Multiple linear regression and semi-log models are employed in the study, and ordinary least squares (OLS) regression is used to estimate parameters and verify the model's accuracy [9]. However, the paper used a small data set of 219 samples. While studying housing mortgage prices, Fan et al. discovered that property rights significantly affect housing prices [10]. Wang et al. Focuses their study on external factors, using a global regression model to analyze the significant spatial distribution pattern of housing prices, taking their adjacency to subway stations into consideration [11].

In this research, nine variables are assessed for their impact on housing prices and model to study the correlation between these factors and housing prices, including housing area, building type, decoration type, building orientation, housing purpose, building type, number of bathrooms, number of living rooms, and number of bedrooms, using multiple linear regression model, to discover the influencing factor for housing prices in Shanghai.

2. Methodology

2.1. Data source

The dataset used in this study is collected from various websites showing Shanghai housing prices data and spans from 2023 to 2024. The dataset contains 395,001 entries, and 48,234 of these were selected as the samples for this study.

2.2. Variable selection

The original dataset is huge and contains many variables with missing values, such as construction time, building type, and building structure. These variables were removed in this study. Ultimately, random sampling was used to obtain the data. The data includes nine variables (housing area, building type, decoration type, building orientation, housing purpose, number of bathrooms, number of living rooms, and number of bedrooms) and one dependent variable (the housing price). The dataset used is described in Table 1:

Table 1. Variables description.

2.3. Method introduction

The multiple linear regression model is employed to compare results with and without considering interaction terms, aiming to compare the importance and accuracy of the two models' results. Ultimately, the optimization of the models is conducted.

The multiple linear regression model falls into the category of linear regression models. The multiple explanatory variables used in the analysis enables it to illustrate the linear relationship between the explanatory variables and the dependent variable [12]. The model estimates multiple parameters through Ordinary Least Squares (OLS), thereby minimizing the sum of squared residuals between the dependent and independent variables.

3. Results and discussion

3.1. Correlation analysis

The analysis in this paper shows that there are many factors influencing housing prices. As shown in the Table 2:

Table 2. Correlation Analysis between Dependent and Independent Variables

The data reveals that living area, decoration type, and building usage are the factors most positively correlated with housing prices. Therefore, it seems that people are particularly interested in the living area, decoration type, and building usage of a house. The number of bathrooms, living rooms, and bedrooms also shows a significant positive correlation with housing prices. Additionally, building type and the age of the house are negatively correlated with housing prices, and this correlation is very significant. In summary, the factors influencing housing prices are comprehensive. Nowadays, people desire a perfect house from various perspectives. After analyzing the Pearson correlation matrix of the factors, a multiple regression analysis is conducted.

3.2. Linear model results

The results of the linear regression are shown in Table 3. The regression coefficients of the multiple linear regression equation model indicate that the area of the house negatively affects its price, while the building type positively affects the price. Houses that are in slab-type apartment buildings are more expensive than those that are not. The decoration type also has a positive impact on housing prices, with luxury-decorated houses being more expensive than non-luxury-decorated ones. The orientation of the house has a significant positive impact on the price as well, with south-facing houses being more expensive than others. The regression coefficient for housing usage is the largest, indicating that residential-use houses are more expensive than non-residential-use houses. The construction age of the house negatively affects the price, but the impact is relatively small. The number of bathrooms, living rooms, and bedrooms positively influences housing prices.

Table 3. Regression Coefficients Table

3.3. Linear regression with interaction terms

Interactions between some independent variables might also affect housing prices; these interaction terms are known as interaction effects. In fact, the number of bedrooms and bathrooms may be somewhat related to the size of the house, meaning the effect of the number of bedrooms and bathrooms on the house price depends on the housing area. Interaction terms between the number of bedrooms and housing area and between the number of bathrooms and housing area are added to the regression equation. The regression results are shown in Tables 4 and 5.

The interaction term between the number of bedrooms and the housing area (x1x5) is significantly negative, while the coefficient for the number of bedrooms is significantly positive. This indicates that the housing area significantly weakens the positive effect of the number of bedrooms on housing prices. When the housing area is larger, the impact of the number of bedrooms on the price may become secondary, as shown in Table 4.

The interaction term between the number of living rooms and the housing area (x1x8) is significantly positive, while the coefficient for the number of living rooms is significantly positive. This suggests that the housing area significantly weakens the positive effect of the number of living rooms on housing prices. When the housing area is larger, the impact of the number of living rooms on the price diminishes. These results are shown in Table 5.

Table 4. Regression Results for Interaction Term Between Number of Bedrooms and Housing Area

Table 5. Regression Results for Interaction Term Between Number of Living Rooms and Housing

4. Conclusion

Ownership of an apartment or house in a major city is a lifelong pursuit for many Chinese urban residents. The soaring housing prices in megacities like Shanghai and Beijing make it difficult for many to afford. This paper examines over 48,000 data sets of Shanghai's real estate transactions from 2023-2024 to understand the factors driving these rising house prices.

This paper uses a multiple linear regression model to compare results with and without considering interaction terms. 9 variables were selected for the analysis. Results reveals shows that Living area, decoration type, and building usage are the factors most positively correlated with housing prices. Therefore, it seems that people are particularly interested in the living area, decoration type, and building usage of a house. The number of bathrooms, living rooms, and bedrooms also shows a significant positive correlation with housing prices. Additionally, building type and the construction age of the house are negatively correlated with housing prices, and this correlation is very significant. Finally, the housing area weakens the positive impact of the number of bathrooms and bedrooms on housing prices.